fastmath.md

a = rand(10^7)

1. Julia hand-written

function mysum(A)
    s = 0.0
    for a in A
        s += a
    end
    return s
end

12s

2. Julia built-in

sum(a)

6s

3. Julia hand-written w/ @fastmath

function mysum_fast(A)
    s = 0.0
    for a in A
        @fastmath s += a
    end
    s
end

6s

4. @fastmath

The for loop

for a in A
    s += a
end

defines a very strict order to the summation: Julia follows exactly what you wrote and adds the elements of A to the result s in the order it iterates. Since floating point numbers aren't associative, a rearrangement here would change the answer — and Julia is loathe to give you different answer than the one you asked for.

You can, however, tell Julia to relax that rule and allow for associativity with the @fastmath macro. This might allow Julia to rearrange the sum in an advantageous manner.